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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: ordinal x0.
Assume H1: ordinal x1.
Assume H2: SNoLt x0 x1.
Apply ordinal_In_Or_Subq with x0, x1, x0x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H3: x0x1.
The subproof is completed by applying H3.
Assume H3: x1x0.
Apply FalseE with x0x1.
Apply SNoLt_irref with x0.
Apply SNoLtLe_tra with x0, x1, x0 leaving 5 subgoals.
Apply ordinal_SNo with x0.
The subproof is completed by applying H0.
Apply ordinal_SNo with x1.
The subproof is completed by applying H1.
Apply ordinal_SNo with x0.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply ordinal_Subq_SNoLe with x1, x0 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H3.